This invention relates to a method of characterizing 3-dimensional flaws of general shape with ultrasound through the use of 2-dimensional tomographic image reconstructions.
By employing the current state-of-the-art ultrasound inspection techniques it is not yet feasible to determine the identity, shape, and orientation of a flaw if its size is smaller than the ultrasound beam diameter. For such a small flaw the composition and geometrical parameters are frequently estimated from their acoustic scattering pattern. In the three-dimensional inverse Born Approximation the back-scattered amplitude A(.omega.,.OMEGA.) of plane acoustic wave incident on an isotropic homogenous flaw in an isotropic homogenous medium can be written in the form: EQU A(.omega., .OMEGA.)=.omega..sup.2 F({.mu.}) S(2.omega./v,.OMEGA.) (1)
where F{.mu.} is a function of {.mu.} which denotes collectively the material parameters of the medium and the flaw, and S(k, .OMEGA.) is equal to the Fourier transform of the characteristic function .rho.(r) of the flaw in the direction .OMEGA. of the incident plane wave (see Rose, J. H. and Krumhansl, J. A., J. Appl. Phys. 50 (1979) 2951, 52). Here the characteristic function .rho.(r) specifies the flaw shape and is defined as equal to 1 inside the flaw and equal to 0 outside. With the substitution k=.omega./v and rearranging, equation (1) can be written in the form EQU S(k,.OMEGA.)=4A(kv/2,.OMEGA.)/[k.sup.2 v.sup.2 F({.mu.)] (2 )
In other words an ultrasonic inspection of a flaw at an angle .OMEGA. yields a line of Fourier components of the characteristic function .rho.(r) of the flaw, with the line oriented in the same direction .OMEGA. in the Fourier space and passing through the origin. This situation is illustrated in FIG. 1, where (x, y, z) denotes spatial coordinates in object space and (k.sub.x, k.sub.y, k.sub.z) denotes spatial frequency coordinates in Fourier space. Therefore inspecting the flaw at all angles in a half space will yield all the Fourier components of .rho.(r), and from these Fourier components .rho.(r) can be reconstructed through 3-dimensional inverse Fourier transformation. The material parameters of the flaw can be determined from pitch catch measurements if desired (see Rose, J. H., and Richardson, J. M., J. Nondestr. Eval., 3 (1982) 45.)
Thus in order to characterize the flaw one has to inspect it from all 4.pi. angles in 3 dimensions and perform an inverse 3-dimensional Fourier transform. Such a procedure involves a number of difficulties: (1) a large amount of data to take and process; (2) some angles may not be accessible to inspection; (3) complications associated with 3-dimensional image reconstructions, such as 3-dimensional interpolation, long computing time, etc. For these reasons the method is usually simplified and restricted to characterize symmetrically shaped flaws, which can be characterized by using only a small number of pulse echoes. This simplified procedure is known as the 1-dimensional inverse Born Approximation (see Rose, J. H. et al, "Inversion of Ultrasonic Scattering Data", Acoustic, Electromagnetic and Elastic Wave Scattering, V. V. Varadan and V. K. Varadan (Eds.), Pergamon, 1980). Though the procedure is simple, it cannot be applied to characterize flaws of more general shape.